1There is a roof , I assume ?
1) You've got 27 coin, each of them is 10 g, except for 1. The 1 different coin is 9 g or 11 g (heavier, or lighter by 1 g). You should use balance scale that compares what's in the two pans. You can get the answer by just comparing groups of coins.
What is the minimum number weighings that can always guarantee to determine the different coin.
2) There is a room with no windows, doors, or any sort of opening, the walls are solid steel 10 feet thick, and you are trapped inside, left only with a saw and a table. How do you escape?
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7 Answers
4@minch : Is there a roof
If no
Then we wud cut the table make steps of it n escape
212) You saw the table in half; but the two halves together; two halves make a whole (hole) and you crawl out through the hole.
11)6 steps.
divide 27 into 3+3+3+3+3+3+3+3+3.
lets call them 31,32..39
now compare 31and 32
then 33and 34
35and 36
37and 38
u have made 4 comparisons,
in this process, stop at the stage where u get an imbalance.
worst case can
1)take u up till the 4th comparison,
2)u can realise that the last one ie 3-9 is faulty
for 1),
now, u have 2 sets which are not equal, either, 37 or 38, compare the heavier one with any standard set of 3s.
if both are balanced, then the fault is 'light'
till now u have made 5 comparisons,
take the faulty 3, spilt into 1+1+1, compare any 2 of them,
if both balance, then the 3rd one at fault, if not then the lighter one at fault.
now, similarly u can proceed if the fault is 'heavy'.
for 2),
split up 39 to 1+1+1
compare any 2, if balanced, compare the 3rd (faulty)one with any of the other standard ones, u get the fault.
if not balanced, compare the lighter one with a standard coin, if found balanced, then, the other one is faulty. else that itself is faulty, and u have the fault.
in both cases, it takes 6 trials.
for the second puzzle, id consider standing up on the table and cutting the roof if it wasn't too thick, or else, make a ladder out of the table and escape out if no roof were present.
cheers!!